1. Field of the Invention
This invention relates to dispersion equalization in multi-oscillators and, more particularly, to active magnetic field tuning for dispersion equalization in a multi-oscillator cavity.
2. Description of the Prior Art
Multi-oscillators have been proposed as a way of overcoming the "lock-in" problem encountered in ring laser gyroscopes. In essence, a multi-oscillator operates as a pair of two-mode ring laser gyroscopes that share a single light cavity. The multi-oscillator cavity sustains a substantially left circularly polarized (LCP) beam pair, comprising one beam propagating within the cavity in the clockwise direction and another in the counterclockwise ("anticlockwise") direction having angular frequencies W.sub.LC and W.sub.LA, respectively. The multi-oscillator cavity further sustains a substantially right circularly polarized (RCP) beam pair comprising counter-propagating beams having angular frequencies W.sub.RC and W.sub.RA. Ideally each beam pair acts independently as a two-mode ring laser gyroscope and senses body rotation by means of the Sagnac effect.
In order to achieve independent operation of two gyroscopes within the same cavity, the two beam pairs, one of LCP light and the other of RCP light, are caused to operate about different frequencies. This separation of frequencies is known as "reciprocal splitting" and is typically on the order bf hundreds of megahertz (MHz) (see FIG. 1A). Early multi-oscillator designs achieved the necessary reciprocal splitting by placing a suitably aligned optically active element in a cavity. More recent designs achieve reciprocal splitting by providing a nonplanar ray path.
With reciprocal splitting invoked, the two pairs of counterpropagating beams function independently, but each still suffers from lock-in. Unlike a two-mode gyro in which lock-in is overcome with a mechanically applied bias such as body dither, the multi-oscillator circumvents the lock-in problem by applying an optical bias to the two gyros so that each operates about a point far removed from the "dead band" where the gyros give no output. This bias is known as "nonreciprocal splitting" and is normally accomplished by a Faraday rotator, an intracavity element made of suitable glass and mounted within an axial magnetic field.
When circularly polarized light passes through a Faraday rotator, it experiences a phase shift that depends on the direction of propagation through the rotator. Thus, the clockwise and anticlockwise beams of each gyro experience different phase shifts, causing them to lase at different frequencies. Typical values for the nonreciprocal splitting in a multi-oscillator are on the order of MHz.
Nonreciprocal splitting can also be achieved by surrounding the gaseous gain medium of the cavity with an axial magnetic field. This phenomenon is known as "Zeeman splitting".
When nonreciprocal splitting is applied to the multi-oscillator in the prescribed manner, the resulting bias shift in the LCP gyro is equal but opposite in sign to the bias shift in the RCP gyro. This yields the four distinct resonant frequencies (or modes) illustrated in FIG. 1A. These include: an LCP clockwise beam (W.sub.LC) having an amplitude (A.sub.LC), an LCP anticlockwise beam (W.sub.LA) having an amplitude (A.sub.LA), an RCP clockwise beam clockwise beam (W.sub.RA) having an amplitude (A.sub.RC), and an RCP anticlockwise beam (W.sub.RA) having an amplitude (A.sub.RA)
When the outputs of the two differently polarized gyros of a multi-oscillator are combined, the resultant signal is doubly sensitive to body rotation but independent of the magnitude of the applied bias. In this way, the differential nature of the multi-oscillator makes it inherently insensitive to many large bias variations.
Unfortunately, however, nonplanar multi-oscillator cavities are susceptible to significant drift errors due to "dispersion", which is a frequency dependent index of refraction associated with the gain of the laser medium used. The four modes of such a cavity are therefore shifted in frequency by different amounts due to the presence of the gain medium, causing undesired drift in cavity output. This condition is shown in the mode diagram of FIG. 1A by the fact that the gain curve 10 is asymmetric, causing the amplitudes of the LCP and RCP laser beams to be unequal. In addition, a helicity dependence (shown in FIG. 1B) may be present. This can cause an amplitude difference between the LCP clockwise mode and the LCP anticlockwise modes and between the RCP clockwise and RCP anticlockwise modes. The helicity dependence of the gain curve is affected by magnetic fields applied to the gain medium.
The phenomenon of dispersion is discussed in U.S. Pat. No. 4,470,701 to Irl W. Smith, which purports to eliminate error due to dispersion by applying a magnetic field to the gain medium at a level proportional to the magnitude of the split in frequency provided by a Faraday rotator. The magnitude of the Faraday bias is measured by optically separating the LCP and RCP beam pairs and averaging the frequencies of the resulting signals. This average is multiplied by appropriate proportionality constants and applied to the coil as a control signal. Unfortunately, the bias control signal calculated in an open loop fashion according to the Smith '701 patent is itself dependent on a number of variables which are not accounted for by the technique disclosed therein. The output of a cavity "corrected" in this way therefore remains subject to the adverse effects of dispersion.
Thus, it is desirable in many applications to provide a system for accurately equalizing dispersion in a multioscillator cavity and thereby eliminating dispersion drift error.